U-shaped development in math: 7-year-olds outperform 9-year-olds on equivalence problems

Area of Science:

• Cognitive Development
• Mathematical Cognition
• Child Psychology

Background:

• Prevailing theories predict a positive association between age and mathematical equivalence problem-solving.
• Change-resistance accounts propose a U-shaped association, with initial performance decline before improvement.

Purpose of the Study:

• To investigate the nature of the association between age (7-11 years) and performance on mathematical equivalence problems.
• To test predictions from prevailing theories against change-resistance accounts.

Main Methods:

• Two studies were conducted with children aged 7-11 years.
• Study 1 involved 87 participants; Study 2 replicated performance decrements with 35 participants.
• Performance on mathematical equivalence problems was assessed across different age groups.

Main Results:

• Results supported the change-resistance account.
• A U-shaped association was observed: performance declined between ages 7 and 9, then improved between ages 9 and 11.
• Performance decrements between ages 7 and 9 were replicated in the second study.

Conclusions:

• The association between age and performance on mathematical equivalence problems is U-shaped.
• Findings challenge theories predicting a simple positive association and support change-resistance explanations.
• Development in mathematical equivalence understanding may involve an initial period of difficulty before improvement.